Finite Group Databasebeta

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C2×C3×C29×D35 #27131824

order12180
isoclinismisoclinic class of D35
automorphism?
homologyAbelianization (H1) = C22×C3×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C29×D35
unambiguous semidirect product(C2×C5)⋊(C3×D7×C29)

Splittings

Fitting, socleC2×C3×C5×C7×C29 ⋊ C2
derived, HallC5×C7 ⋊ C22×C3×C29
HallC3×C5×C7×C29 ⋊ C22
HallC5×C7×C29 ⋊ C22×C3
HallC3×C7×C29 ⋊ C2×D5
HallC3×C5×C29 ⋊ C2×D7
HallC7×C29 ⋊ C2×C3×D5
HallC5×C29 ⋊ C2×C3×D7
HallC3×C5×C7 ⋊ C22×C29
HallC3×C7 ⋊ C2×D5×C29
HallC3×C5 ⋊ C2×D7×C29
SylowC7 ⋊ C2×C3×D5×C29
SylowC5 ⋊ C2×C3×D7×C29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C29D35
commutator, hypocenterC5×C7C22×C3×C29
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C29C2
LCSG ▷ C5×C7
UCSC1 ◁ C2×C3×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3306 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C29×C5⋊(D7⋊C9), C2×C9×C29×D35, C2×C3×C29×C5⋊AGL(1,𝔽7), …
maximal normal subgroup ofC2×C29×C5⋊(D7⋊C9), C2×C9×C29×D35, C2×C3×C29×C5⋊AGL(1,𝔽7), …
maximal quotient ofC2×C9×C29×D35, C3×D3×C29×D35, C2×C32×C29×D35, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 159);